Two-phase equilibria and nucleation barriers near a critical point

A liquid-gas system at temperatures below criticality and densities between the liquid and the gas density at the coexistence curve exhibits equilibrium between a spherical liquid domain and the surrounding gas. This two-phase state is studied for the three-dimensional lattice-gas model, with the use of Monte Carlo methods. In sampling the chemical potential of lattices which are finite but much larger than the correlation length for various densities, the radius $R$ of the liquid cluster is derived from the excess density without any ambiguities in the cluster definition. From the relation between cluster radius and excess chemical potential, information on the universal scaled interface free energy of clusters as a function of $\frac{R}{\xi }$ is obtained, in the range $3\lesssim \frac{R}{\xi }\lesssim 10$, which is also the range of experimental interest. The resulting free-energy barriers against nucleation deviate distinctly from the capillarity approximation in most parts of this regime. At temperatures far below criticality, the present method is shown to agree with the standard approach where a cluster is defined in terms of the contour around occupied lattice sites. Finally, the consequences of our results for experiments and phenomenological droplet models are briefly discussed.